Systems of axon-like circuits for self-assembled and self-controlled growth of bioelectric networks

Abstract

By guiding cell and chemical migration and coupling with genetic mechanisms, bioelectric networks of potentials influence biological pattern formation and are known to have profound effects on growth processes. An abstract model that is amenable to exact analysis has been proposed in the circuit tile assembly model (cTAM) to understand self-assembled and self-controlled growth as an emergent phenomenon that is capable of complex behaviors, like self-replication. In the cTAM, a voltage source represents a finite supply of energy that drives growth until it is unable to overcome randomizing factors in the environment, represented by a threshold. Here, the cTAM is extended to the axon or alternating cTAM model (acTAM) to include a circuit similar to signal propagation in axons, exhibiting time-varying electric signals and a dependence on frequency of the input voltage. The acTAM produces systems of circuits whose electrical properties are coupled to their length as growth proceeds through self-assembly. The exact response is derived for increasingly complex circuit systems as the assembly proceeds. The model exhibits complicated behaviors that elucidate the interactive role of energy, environment, and noise with electric signals in axon-like circuits during biological growth of complex patterns and function.

Logical computation with self-assembling electric circuits

“…Moreover, the bcTAM is implemented with relatively simple circuit components that approximate the DC electric functionality of axons, showing the power inherent in axonal growth. Finally, the relationship between the length of the ladders and the electric potential is known [ 11 , 12 ], and thus, the input voltages can be determined to a given range based on the length of the ladder. Therefore, the bcTAM provides a new model for biological growth with powerful computational capabilities that might produce further understanding of the role of electric phenomena in biological form and function.…”

“…Thus, the electric potential acts similarly to a finite nutrient supply in a bacterial colony, or for that matter, the electric potential in artificial growth processes, like electroplating [10]. Though a nonbiological system, the cTAM achieves life-like properties, such as selfassembled, self-controlled growth [8,9,[11][12][13], and self-replication [14]. Also, the cTAM model is a dynamic model where glues activate when certain criteria are fulfilled.…”

“…The ladder circuits in the cTAM closely resemble those for the propagation of action potentials down axons. This relationship has been more fully explored in [11]. Thus, the bioelectric network that the bcTAM most closely resembles are networks of axons whose growth is influenced by active electric signals, which can elongate axons and change the growth dynamics [17], are potentially important in neural development [17][18][19], and when coupled with gene expression, have a fundamental role in the growth and organization of neural networks [18].…”

“…Thus, the bioelectric network that the bcTAM most closely resembles are networks of axons whose growth is influenced by active electric signals, which can elongate axons and change the growth dynamics [17], are potentially important in neural development [17][18][19], and when coupled with gene expression, have a fundamental role in the growth and organization of neural networks [18]. Our previous works [8,9,[11][12][13][14] investigated electric signal propagation and its impact on dynamic circuit configurations, and this work focuses on the capacity for logical decision-making in the Circuit Tile Assembly Model. The bcTAM model shows the capability of performing Boolean functions in simple, biological mechanisms, such as axon growth.…”

“…The basic cTAM is a self-controlled self-assembly model [8,9], and achieves self-replication with modified electric circuit components in the Replicating Circuit Tile Assembly Model (rcTAM) [14]. Capacitors and time-varying signals are incorporated into the cTAM in [11], termed the Axonal cTAM (acTAM), in which the exact response and signal propagation of the network is calculated. This work adds an additional capability, i.e.…”